Report of the fit

Fit summary

Description: Test fit with the MAP 2021 parameterisation.
Minimiser: ceres
Random seed: 1234
Maximum values allowed for q_T / Q for Drell Yan dataset: 0.2 (0.2 for ATLAS dataset)
Maximum values allowed for q_T / Q for SIDIS dataset: min[ min[ 0.2 / z, 0.5 ] + 0.3 / (z*Q) ], 1 ]
Percentile cut: 5
Parameterisation: MAP22g52
Initial parameters fluctuations: False
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \exp(S_{\rm NP}(\zeta, b_T))\frac{g_1(x) \exp( - g_1(x) \frac{b_T^2}{4}) + \lambda^2 g_{1B}^2(x) ( 1 - g_{1B}(x) \frac{b_T^2}{4}) \exp( - g_{1B}(x) \frac{b_T^2}{4}) + \lambda_2^2 g_{1C}(x) exp( - g_{1C}(x) \frac{b_T^2}{4}) }{ g_1(x) + \lambda^2 g_{1B}^2(x) + \lambda_2^2 g_{1C}(x) }D_{\rm NP}(z,\zeta, b_T)= \exp(S_{\rm NP}(\zeta, b_T))\frac{g_3(z) \exp( - g_3(z) \frac{b_T^2}{4z^2}) + \frac{\lambda_F}{z^2} g_{3B}^2(z) \big ( 1 - g_{3B}(z) \frac{b_T^2}{4z^2} \big ) \exp( - g_{3B}(z) \frac{b_T^2}{4z^2}) }{ g_3(z) + \frac{\lambda_F}{z^2} g_{3B}^2(z) }S_{\rm NP} = \exp\left[ - g_2^2 \frac{b_T^2}{4} \log \big (\frac{\zeta}{Q_0^2}\big ) \right]g_{1,1B,1C}(x) = N_{1,1B,1C} \frac{x^{\sigma_{1,2,3}}(1-x)^{\alpha^2_{1,2,3}}}{\hat{x}^{\sigma_{1,2,3}}(1-\hat{x})^{\alpha^2_{1,2,3}}}g_{3,3B}(z) = N_{3,3B} \frac{(z^{\beta_{1,2}}+\delta^2_{1,2})(1-z)^{\gamma^2_{1,2}}}{(\hat{z}^{\beta_{1,2}}+\delta^2_{1,2})(1-\hat{z})^{\gamma^2_{1,2}}}Q_0^2 = 1\;{\rm GeV}^2\hat{x} = 0.1\hat{z} = 0.5 t_0 prescription: True

g_2 N_1 \alpha_1 \sigma_1 \lambda N_3 \beta_1 \delta_1 \gamma_1 \lambda_F N_{3B} N_{1B} N_{1C} \lambda_2 \alpha_2 \alpha_3 \sigma_2 \sigma_3 \beta_2 \delta_2 \gamma_2
0.2496226714249004 0.3020626592370139 2.666844840265717 2.102584088709731 55.07070253010257 0.005080413995163261 7.921481547106262 0.04015419519659606 1.689458640435588 0.3739836783648748 0.1252334678836607 0.00494775552126632 8.499617210290662e-05 0.01417965874844849 2.091301439926813 2.508762142075416 0.7190865974867623 10.81263317134855 2.587650914497618 0.2206893632340438 1.102709259848706

Theory summary

Collinear PDF set: MMHT2014nnlo68cl member 0
Collinear FF set: DSS14_NLO_Pip member 0
Collinear FF set: DSS14_NLO_Pim member 0
Collinear FF set: DSS17_NLO_KaonPlus member 0
Collinear FF set: DSS17_NLO_KaonMinus member 0
b^* prescription: bstarmin
Perturbative order: N3LL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 224
\chi_{0}^2 = 1.3575
\chi_{mean}^2 = 1.3575
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.3729 \pm 0.0129
\langle E \rangle \pm \sigma_{E} = 2.3569 \pm 0.1279

Parameters

Parameter Central replica Average over replicas Fixed
g_2 0.24962267 0.24677103 \pm 0.00922077 False
N_1 0.30206266 0.33420345 \pm 0.05882246 False
\alpha_1 2.6668448 2.45703282 \pm 0.20760685 False
\sigma_1 2.1025841 1.73285923 \pm 0.31708634 False
\lambda 55.070703 706.95611794 \pm 1851.64347136 False
N_3 0.005080414 0.00507694 \pm 5.942e-05 False
\beta_1 7.9214815 7.92333834 \pm 0.03692426 False
\delta_1 0.040154195 0.04015742 \pm 0.0001932 False
\gamma_1 1.6894586 1.68834679 \pm 0.01027721 False
\lambda_F 0.37398368 0.37374892 \pm 0.00202261 False
N_{3B} 0.12523347 0.1252403 \pm 0.00051155 False
N_{1B} 0.0049477555 0.01924069 \pm 0.0184925 False
N_{1C} 8.4996172e-05 7.143e-05 \pm 0.00015141 False
\lambda_2 0.014179659 0.01028615 \pm 0.01954051 False
\alpha_2 2.0913014 6.65115976 \pm 4.73225431 False
\alpha_3 2.5087621 2.13931407 \pm 1.06578512 False
\sigma_2 0.7190866 4.62109869 \pm 4.53470634 False
\sigma_3 10.812633 11.80637269 \pm 1.10223703 False
\beta_2 2.5876509 2.58605514 \pm 0.02011599 False
\delta_2 0.22068936 0.22075037 \pm 0.00080128 False
\gamma_2 1.1027093 1.10262273 \pm 0.00180724 False
Fitted parameter correlation matrix

Fit properties

Global \chi^2 distribution
Global error function distribution
g_2 distribution
N_1 distribution
\alpha_1 distribution
\sigma_1 distribution
\lambda distribution
N_3 distribution
\beta_1 distribution
\delta_1 distribution
\gamma_1 distribution
\lambda_F distribution
N_{3B} distribution
N_{1B} distribution
N_{1C} distribution
\lambda_2 distribution
\alpha_2 distribution
\alpha_3 distribution
\sigma_2 distribution
\sigma_3 distribution
\beta_2 distribution
\delta_2 distribution
\gamma_2 distribution

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 1.199 0.195 1.394
E605_Q_8_9 8 2.449 0.124 2.572
E605_Q_10.5_11.5 10 0.42 0.035 0.456
E605_Q_11.5_13.5 12 0.665 0.292 0.957
E605_Q_13.5_18 13 0.976 0.665 1.641
E772_Q_5_6 4 1.725 0.735 2.46
E772_Q_6_7 5 1.436 0.675 2.111
E772_Q_7_8 6 2.888 1.342 4.229
E772_Q_8_9 6 2.722 1.201 3.923
E772_Q_11_12 9 0.941 0.022 0.964
E772_Q_12_13 10 1.174 0.003 1.177
E772_Q_13_14 7 2.419 0.36 2.779
E772_Q_14_15 6 0.289 0.002 0.291
E288_200_Q_4_5 4 0.382 0.212 0.594
E288_200_Q_5_6 5 1.24 0.131 1.37
E288_200_Q_6_7 6 0.205 0.191 0.396
E288_200_Q_7_8 7 0.154 0.223 0.377
E288_200_Q_8_9 8 0.491 0.276 0.767
E288_300_Q_4_5 4 0.538 0.011 0.549
E288_300_Q_5_6 5 1.127 0.004 1.131
E288_300_Q_6_7 6 0.532 0.001 0.533
E288_300_Q_7_8 7 0.06 0.003 0.063
E288_300_Q_8_9 8 1.028 0.006 1.034
E288_300_Q_11_12 9 0.32 0.018 0.338
E288_400_Q_5_6 5 0.493 0.085 0.578
E288_400_Q_6_7 6 0.207 0.07 0.277
E288_400_Q_7_8 7 0.045 0.081 0.126
E288_400_Q_8_9 8 0.606 0.084 0.69
E288_400_Q_11_12 11 0.668 0.053 0.721
E288_400_Q_12_13 12 0.961 0.02 0.982
E288_400_Q_13_14 12 0.709 0.039 0.747
PHENIX_200 2 4.481 2.505 6.985
STAR_510 7 1.478 0.025 1.503
CDF_RunI 25 0.674 0.056 0.73
CDF_RunII 26 1.746 0.04 1.786
D0_RunI 12 0.769 0.035 0.804
D0_RunII 5 1.244 0.517 1.761
D0_RunIImu 3 5.248 0.7 5.948
LHCb_7TeV 7 1.497 0.234 1.732
LHCb_8TeV 7 0.539 0.056 0.595
LHCb_13TeV 7 1.498 0.05 1.548
CMS_7TeV 4 2.114 0.055 2.169
CMS_8TeV 4 1.551 0.003 1.554
CMS_13TeV_y_0_0.4 14 0.166 0.025 0.191
CMS_13TeV_y_0.4_0.8 14 0.101 0.018 0.118
CMS_13TeV_y_0.8_1.2 14 0.136 0.003 0.139
CMS_13TeV_y_1.2_1.6 14 0.1 0.0 0.1
CMS_13TeV_y_1.6_2.4 14 0.273 0.017 0.291
ATLAS_7TeV_y_0_1 6 6.784 0.331 7.115
ATLAS_7TeV_y_1_2 6 3.556 1.008 4.564
ATLAS_7TeV_y_2_2.4 6 1.716 0.708 2.424
ATLAS_8TeV_y_0_0.4 6 4.593 0.347 4.94
ATLAS_8TeV_y_0.4_0.8 6 4.68 0.289 4.968
ATLAS_8TeV_y_0.8_1.2 6 1.796 0.114 1.91
ATLAS_8TeV_y_1.2_1.6 6 1.6 0.093 1.692
ATLAS_8TeV_y_1.6_2 6 1.508 0.07 1.578
ATLAS_8TeV_y_2_2.4 6 0.494 0.182 0.676
ATLAS_8TeV_Q_46_66 4 1.452 1.239 2.691
ATLAS_8TeV_Q_116_150 8 0.625 0.005 0.629
ATLAS_13TeV 6 3.084 0.466 3.55
Total 484 1.167 0.19 1.357
Mean-replica \chi^2’s:
Experiment Number of points \chi_{D}^2 \chi_{\lambda}^2 \chi^2
E605_Q_7_8 7 1.199 0.195 1.394
E605_Q_8_9 8 2.449 0.124 2.572
E605_Q_10.5_11.5 10 0.42 0.035 0.456
E605_Q_11.5_13.5 12 0.665 0.292 0.957
E605_Q_13.5_18 13 0.976 0.665 1.641
E772_Q_5_6 4 1.725 0.735 2.46
E772_Q_6_7 5 1.436 0.675 2.111
E772_Q_7_8 6 2.888 1.342 4.229
E772_Q_8_9 6 2.722 1.201 3.923
E772_Q_11_12 9 0.941 0.022 0.964
E772_Q_12_13 10 1.174 0.003 1.177
E772_Q_13_14 7 2.419 0.36 2.779
E772_Q_14_15 6 0.289 0.002 0.291
E288_200_Q_4_5 4 0.382 0.212 0.594
E288_200_Q_5_6 5 1.24 0.131 1.37
E288_200_Q_6_7 6 0.205 0.191 0.396
E288_200_Q_7_8 7 0.154 0.223 0.377
E288_200_Q_8_9 8 0.491 0.276 0.767
E288_300_Q_4_5 4 0.538 0.011 0.549
E288_300_Q_5_6 5 1.127 0.004 1.131
E288_300_Q_6_7 6 0.532 0.001 0.533
E288_300_Q_7_8 7 0.06 0.003 0.063
E288_300_Q_8_9 8 1.028 0.006 1.034
E288_300_Q_11_12 9 0.32 0.018 0.338
E288_400_Q_5_6 5 0.493 0.085 0.578
E288_400_Q_6_7 6 0.207 0.07 0.277
E288_400_Q_7_8 7 0.045 0.081 0.126
E288_400_Q_8_9 8 0.606 0.084 0.69
E288_400_Q_11_12 11 0.668 0.053 0.721
E288_400_Q_12_13 12 0.961 0.02 0.982
E288_400_Q_13_14 12 0.709 0.039 0.747
PHENIX_200 2 4.481 2.505 6.985
STAR_510 7 1.478 0.025 1.503
CDF_RunI 25 0.674 0.056 0.73
CDF_RunII 26 1.746 0.04 1.786
D0_RunI 12 0.769 0.035 0.804
D0_RunII 5 1.244 0.517 1.761
D0_RunIImu 3 5.248 0.7 5.948
LHCb_7TeV 7 1.497 0.234 1.732
LHCb_8TeV 7 0.539 0.056 0.595
LHCb_13TeV 7 1.498 0.05 1.548
CMS_7TeV 4 2.114 0.055 2.169
CMS_8TeV 4 1.551 0.003 1.554
CMS_13TeV_y_0_0.4 14 0.166 0.025 0.191
CMS_13TeV_y_0.4_0.8 14 0.101 0.018 0.118
CMS_13TeV_y_0.8_1.2 14 0.136 0.003 0.139
CMS_13TeV_y_1.2_1.6 14 0.1 0.0 0.1
CMS_13TeV_y_1.6_2.4 14 0.273 0.017 0.291
ATLAS_7TeV_y_0_1 6 6.784 0.331 7.115
ATLAS_7TeV_y_1_2 6 3.556 1.008 4.564
ATLAS_7TeV_y_2_2.4 6 1.716 0.708 2.424
ATLAS_8TeV_y_0_0.4 6 4.593 0.347 4.94
ATLAS_8TeV_y_0.4_0.8 6 4.68 0.289 4.968
ATLAS_8TeV_y_0.8_1.2 6 1.796 0.114 1.91
ATLAS_8TeV_y_1.2_1.6 6 1.6 0.093 1.692
ATLAS_8TeV_y_1.6_2 6 1.508 0.07 1.578
ATLAS_8TeV_y_2_2.4 6 0.494 0.182 0.676
ATLAS_8TeV_Q_46_66 4 1.452 1.239 2.691
ATLAS_8TeV_Q_116_150 8 0.625 0.005 0.629
ATLAS_13TeV 6 3.084 0.466 3.55
Total 484 1.167 0.19 1.357
Average-over-replicas \chi^2’s:
Experiment Number of points \chi^2
E605_Q_7_8 7 1.385 \pm 0.293
E605_Q_8_9 8 2.505 \pm 0.389
E605_Q_10.5_11.5 10 0.476 \pm 0.033
E605_Q_11.5_13.5 12 0.961 \pm 0.037
E605_Q_13.5_18 13 1.648 \pm 0.082
E772_Q_5_6 4 2.586 \pm 0.577
E772_Q_6_7 5 1.899 \pm 0.485
E772_Q_7_8 6 3.985 \pm 0.473
E772_Q_8_9 6 3.763 \pm 0.37
E772_Q_11_12 9 0.972 \pm 0.037
E772_Q_12_13 10 1.17 \pm 0.044
E772_Q_13_14 7 2.8 \pm 0.31
E772_Q_14_15 6 0.293 \pm 0.033
E288_200_Q_4_5 4 0.687 \pm 0.216
E288_200_Q_5_6 5 1.551 \pm 0.289
E288_200_Q_6_7 6 0.428 \pm 0.115
E288_200_Q_7_8 7 0.409 \pm 0.201
E288_200_Q_8_9 8 0.75 \pm 0.182
E288_300_Q_4_5 4 0.638 \pm 0.134
E288_300_Q_5_6 5 1.231 \pm 0.19
E288_300_Q_6_7 6 0.578 \pm 0.137
E288_300_Q_7_8 7 0.072 \pm 0.018
E288_300_Q_8_9 8 1.007 \pm 0.091
E288_300_Q_11_12 9 0.383 \pm 0.093
E288_400_Q_5_6 5 0.766 \pm 0.233
E288_400_Q_6_7 6 0.374 \pm 0.133
E288_400_Q_7_8 7 0.167 \pm 0.05
E288_400_Q_8_9 8 0.795 \pm 0.138
E288_400_Q_11_12 11 0.718 \pm 0.122
E288_400_Q_12_13 12 0.987 \pm 0.051
E288_400_Q_13_14 12 0.794 \pm 0.08
PHENIX_200 2 7.7 \pm 1.435
STAR_510 7 1.529 \pm 0.043
CDF_RunI 25 0.737 \pm 0.027
CDF_RunII 26 1.802 \pm 0.154
D0_RunI 12 0.815 \pm 0.033
D0_RunII 5 1.822 \pm 0.144
D0_RunIImu 3 5.836 \pm 0.302
LHCb_7TeV 7 1.773 \pm 0.077
LHCb_8TeV 7 0.607 \pm 0.036
LHCb_13TeV 7 1.553 \pm 0.159
CMS_7TeV 4 2.171 \pm 0.006
CMS_8TeV 4 1.561 \pm 0.035
CMS_13TeV_y_0_0.4 14 0.191 \pm 0.017
CMS_13TeV_y_0.4_0.8 14 0.119 \pm 0.009
CMS_13TeV_y_0.8_1.2 14 0.138 \pm 0.022
CMS_13TeV_y_1.2_1.6 14 0.103 \pm 0.008
CMS_13TeV_y_1.6_2.4 14 0.301 \pm 0.015
ATLAS_7TeV_y_0_1 6 7.152 \pm 0.443
ATLAS_7TeV_y_1_2 6 4.607 \pm 0.062
ATLAS_7TeV_y_2_2.4 6 2.465 \pm 0.057
ATLAS_8TeV_y_0_0.4 6 4.91 \pm 0.349
ATLAS_8TeV_y_0.4_0.8 6 4.981 \pm 0.217
ATLAS_8TeV_y_0.8_1.2 6 1.961 \pm 0.123
ATLAS_8TeV_y_1.2_1.6 6 1.739 \pm 0.068
ATLAS_8TeV_y_1.6_2 6 1.568 \pm 0.121
ATLAS_8TeV_y_2_2.4 6 0.664 \pm 0.046
ATLAS_8TeV_Q_46_66 4 2.722 \pm 0.141
ATLAS_8TeV_Q_116_150 8 0.631 \pm 0.007
ATLAS_13TeV 6 3.59 \pm 0.223
Total 484 1.373 \pm 0.013

TMDs in k_\perp or P_\perp space

TMD PDF of the u at Q = 2 GeV and x = 0.001
TMD PDF of the u at Q = 2 GeV and x = 0.01
TMD PDF of the u at Q = 2 GeV and x = 0.1
TMD PDF of the u at Q = 10 GeV and x = 0.001
TMD PDF of the u at Q = 10 GeV and x = 0.01
TMD PDF of the u at Q = 10 GeV and x = 0.1
TMD PDF of the u at Q = 100 GeV and x = 0.001
TMD PDF of the u at Q = 100 GeV and x = 0.01
TMD PDF of the u at Q = 100 GeV and x = 0.1

Data-theory comparison

E605_Q_7_8 data-theory comparison
E605_Q_8_9 data-theory comparison
E605_Q_10.5_11.5 data-theory comparison
E605_Q_11.5_13.5 data-theory comparison
E605_Q_13.5_18 data-theory comparison
E772_Q_5_6 data-theory comparison
E772_Q_6_7 data-theory comparison
E772_Q_7_8 data-theory comparison
E772_Q_8_9 data-theory comparison
E772_Q_11_12 data-theory comparison
E772_Q_12_13 data-theory comparison
E772_Q_13_14 data-theory comparison
E772_Q_14_15 data-theory comparison
E288_200_Q_4_5 data-theory comparison
E288_200_Q_5_6 data-theory comparison
E288_200_Q_6_7 data-theory comparison
E288_200_Q_7_8 data-theory comparison
E288_200_Q_8_9 data-theory comparison
E288_300_Q_4_5 data-theory comparison
E288_300_Q_5_6 data-theory comparison
E288_300_Q_6_7 data-theory comparison
E288_300_Q_7_8 data-theory comparison
E288_300_Q_8_9 data-theory comparison
E288_300_Q_11_12 data-theory comparison
E288_400_Q_5_6 data-theory comparison
E288_400_Q_6_7 data-theory comparison
E288_400_Q_7_8 data-theory comparison
E288_400_Q_8_9 data-theory comparison
E288_400_Q_11_12 data-theory comparison
E288_400_Q_12_13 data-theory comparison
E288_400_Q_13_14 data-theory comparison
PHENIX_200 data-theory comparison
STAR_510 data-theory comparison
CDF_RunI data-theory comparison
CDF_RunII data-theory comparison
D0_RunI data-theory comparison
D0_RunII data-theory comparison
D0_RunIImu data-theory comparison
LHCb_7TeV data-theory comparison
LHCb_8TeV data-theory comparison
LHCb_13TeV data-theory comparison
CMS_7TeV data-theory comparison
CMS_8TeV data-theory comparison
CMS_13TeV_y_0_0.4 data-theory comparison
CMS_13TeV_y_0.4_0.8 data-theory comparison
CMS_13TeV_y_0.8_1.2 data-theory comparison
CMS_13TeV_y_1.2_1.6 data-theory comparison
CMS_13TeV_y_1.6_2.4 data-theory comparison
ATLAS_7TeV_y_0_1 data-theory comparison
ATLAS_7TeV_y_1_2 data-theory comparison
ATLAS_7TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_y_0_0.4 data-theory comparison
ATLAS_8TeV_y_0.4_0.8 data-theory comparison
ATLAS_8TeV_y_0.8_1.2 data-theory comparison
ATLAS_8TeV_y_1.2_1.6 data-theory comparison
ATLAS_8TeV_y_1.6_2 data-theory comparison
ATLAS_8TeV_y_2_2.4 data-theory comparison
ATLAS_8TeV_Q_46_66 data-theory comparison
ATLAS_8TeV_Q_116_150 data-theory comparison
ATLAS_13TeV data-theory comparison